Pith Number

pith:RIZG2ZKA

pith:2017:RIZG2ZKA7OYWTP7AAMXD5JJ2CX

not attested not anchored not stored refs pending

Total Betti numbers of modules of finite projective dimension

Mark E. Walker

arxiv:1702.02560 v2 · 2017-02-08 · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RIZG2ZKA7OYWTP7AAMXD5JJ2CX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:43:08.764658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a326d6540fbb169bfe0032e3ea53a15e784be666237d01c1ace97a5cd5664aa

Aliases

arxiv: 1702.02560 · arxiv_version: 1702.02560v2 · doi: 10.48550/arxiv.1702.02560 · pith_short_12: RIZG2ZKA7OYW · pith_short_16: RIZG2ZKA7OYWTP7A · pith_short_8: RIZG2ZKA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RIZG2ZKA7OYWTP7AAMXD5JJ2CX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8a326d6540fbb169bfe0032e3ea53a15e784be666237d01c1ace97a5cd5664aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef95c837197cd37b025d94b8df8df479654e4403a75b04e7e2e8f636c2f1ee44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-02-08T18:50:25Z",
    "title_canon_sha256": "60394e2fd192c63c9d1538140a96570c765e8be9b81701f4787c4e9e7242853b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.02560",
    "kind": "arxiv",
    "version": 2
  }
}